Discrete mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2011
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 465 S. Ill., graph. Darst. 24 cm |
| ISBN: | 1441980466 9781441980465 |
Staff View
MARC
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| 100 | 1 | |a Gallier, Jean H. |d 1949- |e Verfasser |0 (DE-588)122585615 |4 aut | |
| 245 | 1 | 0 | |a Discrete mathematics |c Jean Gallier |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2011 | |
| 300 | |a XIII, 465 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Informatik | |
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Record in the Search Index
| _version_ | 1804145591125540864 |
|---|---|
| adam_text | Contents
Mathematical Reasoning, Proof Principles, and Logic
..............
I
1.
1 Introduction
............................................... 1
1.2
Inference Rules, Deductions, Proof Systems
.
Y^ and
.
V&£
..... 2
1.3
Adding
Л,
V, X; The Proof Systems
.
ί^·Α-νΛ
and
.
Γ(^·Λν1
... 19
1.4
Clearing Up Differences Among Rules Involving _L
.............. 28
1.5 De
Morgan Laws and Other Rules of Classical Logic
............. 32
1.6
Formal Versus Informal Proofs; Some Examples
................ 34
1.7
Truth Values Semantics for Classical Logic
..................... 40
1.8
Kripke Models for Intuitionistic Logic
......................... 43
1.9
Adding Quantifiers: The Proof Systems
.
jf=*A vV·3
ί ^.Λ.ν.ν.3.χ
............................................
45
LIO
First-Order Theories
........................................ 58
1.11
Decision Procedures, Proof Normalization, Counterexamples
...... 64
1.12
Basics Concepts of Set Theory
............................... 70
1.13
Summary
................................................. 79
Problems
...................................................... 82
References
.....................................................100
Relations, Functions, Partial Functions
...........................101
2.1
What is a Function?
.........................................101
2.2
Ordered Pairs, Cartesian Products, Relations, etc
.................104
2.3
Induction Principles on
N....................................109
2.4
Composition of Relations and Functions
.......................117
2.5
Recursion on
N............................................118
2.6
Inverses of Functions and Relations
...........................121
2.7
Injections. Surjections. Bijections. Permutations
.................
1
24
2.8
Direct Image and Inverse Image
..............................128
2.9
Equi numerosi
ty;
Pigeonhole Principle;
Schröder—Bernstein.......129
2.10
An Amazing Surjection: Hubert s Space-Filling Curve
...........141
2.11
Strings, Multisets. Indexed Families
...........................143
2.12
Summary
.................................................147
xii Contents
Problems ......................................................149
References.....................................................
164
3
Graphs, Part I: Basic Notions
....................................165
3.1
Why Graphs? Some Motivations
..............................165
3.2
Directed Graphs
............................................167
3.3
Path in Digraphs, Strongly Connected Components
..............171
3.4
Undirected Graphs, Chains, Cycles, Connectivity
................182
3.5
Trees and
Arborescences
....................................189
3.6
Minimum (or Maximum) Weight Spanning Trees
................194
3.7
Summary
.................................................200
Problems
......................................................201
References
.....................................................203
4
Some Counting Problems; Multinomial Coefficients
................205
4.1
Counting Permutations and Functions
.........................205
4.2
Counting Subsets of Size k Multinomial Coefficients
............208
4.3
Some Properties of the Binomial Coefficients
...................217
4.4
The Principle of Inclusion- Exclusion
..........................229
4.5
Summary
.................................................237
Problems
......................................................238
References
.....................................................255
5
Partial Orders, GCDs, RSA, Lattices
257
5.1
Partial Orders
..............................................257
5.2
Lattices and Tarski s Fixed-Point Theorem
.....................263
5.3
Well-Founded Ordenngs and Complete Induction
...............269
5.4
Unique Prime Factorization in
Ћ
and GCDs
....................278
5.5
Dinchlet s Diophantine Approximation Theorem
................288
5.6
Equivalence Relations and Partitions
..........................291
5.7
Transitive Closure, Reflexive and Transitive Closure
.............295
5.8
Fibonacci and Lucas Numbers; Mersenne Primes
................296
5.9
Public Key Cryptography; The RSA System
....................309
5.10
Correctness of The RSA System
..............................314
5.11
Algorithms for Computing Powers and Inverses Modulo
m
........318
5.12
Finding Large Primes, Signatures; Safety of RSA
................322
5.13
Distributive Lattices, Boolean Algebras, Heyting Algebras
........327
5.14
Summary
.................................................337
Problems
......................................................340
References
.....................................................362
6
Graphs, Part
П:
More Advanced Notions
.........................365
6.1
F-Cycles, Cocycles, Cotrees, Flows, and Tensions
...............365
6.2
Incidence and Adjacency Matrices of a Graph
...................381
6.3
Eulenan and Hamiltonian Cycles
.............................386
6.4
Network Flow Problems; The Max-Flow Mm-Cut Theorem
.......391
Contents xiii
6.5 Matchings,
Coverings, Bipartite Graphs
........................409
6.6
Planar Graphs
.............................................418
6.7
Summary
.................................................435
Problems
......................................................439
References
.....................................................447
Symbol Index
......................................................449
Index
..................................·...........................453
|
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| bvnumber | BV037314556 |
| classification_rvk | SK 110 SK 180 SK 950 |
| ctrlnum | (OCoLC)707153739 (DE-599)BSZ337304998 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037314556 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:53Z |
| institution | BVB |
| isbn | 1441980466 9781441980465 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022468892 |
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| physical | XIII, 465 S. Ill., graph. Darst. 24 cm |
| publishDate | 2011 |
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| publishDateSort | 2011 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Gallier, Jean H. 1949- Verfasser (DE-588)122585615 aut Discrete mathematics Jean Gallier New York [u.a.] Springer 2011 XIII, 465 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Universitext Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Computer science / Mathematics (DE-588)4123623-3 Lehrbuch gnd-content Diskrete Mathematik (DE-588)4129143-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-8047-2 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022468892&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallier, Jean H. 1949- Discrete mathematics Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4123623-3 |
| title | Discrete mathematics |
| title_auth | Discrete mathematics |
| title_exact_search | Discrete mathematics |
| title_full | Discrete mathematics Jean Gallier |
| title_fullStr | Discrete mathematics Jean Gallier |
| title_full_unstemmed | Discrete mathematics Jean Gallier |
| title_short | Discrete mathematics |
| title_sort | discrete mathematics |
| topic | Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Informatik Mathematik Diskrete Mathematik Lehrbuch |
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